Pressure Law

• Found by Joseph Louis Gay-Lussac in 1808
• The pressure of a fixed mass of gas is directly proportional to its absolute temperature given that volume remains constant:

$$ \begin{equation}\begin{aligned} P&\propto T\\ P&=kT\ OR\\ \frac{P}{T}&=k\\ \end{aligned}\end{equation} $$

Thus we can have $\frac{P_1}{T_1}=k$ and $\frac{P_2}{T_2}=k$. Combining these two we get: $$ \begin{equation}\begin{aligned} \frac{P_1}{T_1}=\frac{P_2}{T_2}\\ \end{aligned}\end{equation} $$ Where $P_1$ is the pressure associated with the temperature $T_1$ and $P_2$ is associated with $T_2$.

Example

If the pressure in a car tire is $180\ kPa$ at $27\degree C$, what will be the pressure if the temperature rises to $37\degree C$?

Mission details

Find the initial temperature of a gas where the pressure of $150\ kPa$ is raised to $250\ kPa$ at which point it has a temperature of $182\degree C$.